Online Algorithmic Recourse by Collective Action

TL;DR

The paper addresses recourse under online model updates, proposing Online Algorithmic Recourse (OAR) where data subjects perturb training data to influence the online learning of $\theta$ through a bi-level optimization. It demonstrates that coordinated, collective perturbations can yield better target outcomes for a query subject than isolated perturbations, using simple nearest-centroid experiments on Iris and MNIST embeddings. This highlights a potential for group-driven influence over deployed systems that learn online, with implications for fairness, robustness, and require understanding of how training-data dynamics shape automated decisions. The work also connects to adversarial training, data poisoning, and protective optimization frameworks, pointing to rich directions for future research, including broader actionability constraints and black-box scenarios.

Abstract

Research on algorithmic recourse typically considers how an individual can reasonably change an unfavorable automated decision when interacting with a fixed decision-making system. This paper focuses instead on the online setting, where system parameters are updated dynamically according to interactions with data subjects. Beyond the typical individual-level recourse, the online setting opens up new ways for groups to shape system decisions by leveraging the parameter update rule. We show empirically that recourse can be improved when users coordinate by jointly computing their feature perturbations, underscoring the importance of collective action in mitigating adverse automated decisions.

Figures (2)

• Figure 1: Online algorithmic recourse under a nearest-centroid classifier. Left: A nearest-centroid classifier with parameters ${\theta = \{\mu_1, \mu_2, \mu_3\}}$ is fit to 20 data subjects, with features $\mathbf{X}$ (circles) and class labels $\mathbf{Y}$ (circle colors). A query subject$X_\dagger$ seeks to change their prediction under this model to $\tilde{Y}_\dagger = 1$. The query subject can exercise individual recourse by applying the best perturbation $\delta$ with $||\delta|| \leq \epsilon$ towards this end, moving $X_\dagger+\delta$ towards the decision boundary separating $\hat{Y} = 1$ from $\hat{Y} = 2$. Right: Another means of recourse is to have all data subjects coordinate by applying perturbations $\Delta = [\delta_1 \ldots \delta_N]^T$ with ${||\delta_i|| \leq \epsilon \ \forall \ i}$ in order to help the query subject. Note that this changes the model's decision boundary, as the centroids $\{\mu_k\}$ are fit to the perturbed data $(\mathbf{X}+\Delta, \mathbf{Y})$. This collective recourse is more effective in this instance, as we see that once the model fits new centroids to the perturbed training data, $X_\dagger$ lies on the desired side of the model decision boundary. Data in this example come from first two features of the UCI-Iris dataset.
• Figure 2: Measuring success of recourse according to model loss for query goal class $\tilde{Y}_\dagger$ evaluated at query input $X_\dagger$ (the lower the better). The model is a nearest centroid classifier. We find that on UCI-Iris (left), and MNIST (right), collective recourse is more effective than individual recourse at a given $\epsilon$ budget.